A theory that describes how matter produces and responds to the geometry of space and time. It was first published by Einstein in 1915 and is currently used to study the structure and evolution of the universe, as well as having practical applications like GPS.

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asymptotic curvature of the universe and correlation with local curvature

There is not-so-rough evidence that at very large scale the universe is flat. However we see everywhere that there are local lumps of matter with positive curvature. So i have several questions ...
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1answer
148 views

Does the positive mass conjecture indicate a necessity of interactions in our universe?

The positive mass conjecture was proved by Schoen and Yau and later reproved by Witten. Total mass in a gravitating system must be positive except in the case of flat Minkowski space, where energy is ...
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1answer
448 views

Can the Universe create itself?--Is Gott's Use of CTC in Planck time or less valid?

My question is the title of a 1991 paper by Richard Gott and Li-Xin Li: http://arxiv.org/abs/astro-ph/9712344 and is also a subject of his popular book, "Time Travel in Einstein's Universe" Ultimately ...
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5answers
259 views

High-spin neutron star

Suppose a large neutron star were to be spun-up by a particular pattern of mass-accretion. The increased centrifugal force could presumably mitigate the increased gravity thus delaying gravitational ...
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6answers
2k views

Is the Planck length Lorentz invariant?

The planck length is defined as $l_P = \sqrt{\frac{\hbar G}{c^3}}$. So it is a combination of the constants $c, h, G$ which I believe are all Lorentz invariants. So I think the Planck length should ...
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2answers
493 views

Existence and uniqueness of solutions for Einstein equations

Now that an equivalence of Navier Stokes and Einstein equations has been established, and it is known solutions to Einstein-Maxwell-Boltzmann exist and are unique, and it is known that Einstein ...
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5answers
319 views

Empty universe in the past, non-empty in the future

My question is the following. Are there solutions to the Einstein field equations, which have the property that there is a hypersurface of constant time and to the past of that surface space is empty ...
3
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1answer
526 views

What is a maximal analytic extension?

Can someone explain (as rigorously as possible) what is involved in analytically continuing, say, the Schwarzschild solution to the Kruskal manifold? I understand the two metrics separately but I'm ...
13
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4answers
2k views

Newton's Bucket

Newton's Bucket This thought experiment is originally due to Sir Isaac Newton. We have a sphere of water floating freely in an opaque box in intergalactic space, held together by surface tension and ...
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5answers
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What is a good mathematical description of the Non-renormalizability of gravity?

By now everybody knows that gravity is non-renormalizable, what is often lacking is a simplified mathematical description of what that means. Can anybody provide such a description?
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3answers
599 views

Do singularities have a “real” as opposed to mathematical or idealized existence?

I was thinking of, for example a Schwarzchild metric at r=0, i.e. the gravitational singularity, a point of infinite density. I realise that there are different types of singularities--timelike, ...
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5answers
3k views

How do I calculate the perturbations to the metric determinant?

I am trying to calculate sqrt(-g) in terms of a background metric and metric perturbations, to second order in the perturbations. I know how to expand tensors that depend on the metric, but I don't ...
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1answer
303 views

Measurement of kaluza-klein radion field gradient?

I've been very impressed to learn about kaluza-klein theory and compactification strategies. I would like to read more about this but in the meantime i'm curious about 2 different points. I have the ...
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4answers
434 views

The Matter-Vacuum Boundary in General Relativity

A previous Stack question (before I joined) asking about continuity in GR received replies which suggested that Curvature would be discontinuous at say a planetary boundary (assume no atmosphere for ...
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8answers
680 views

Flat space limit of the Schwarzschild metric and Hawking temperature

The Schwarzschild metric reduces to the Minkowski metric in the limit of vanishing $M$, but the Hawking temperature which is proportional to $1/M$ diverges in the same limit. This would imply that ...
6
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2answers
1k views

Why does pressure act as a source for the gravitational field?

I'm asking for a qualitative explanation if there is one. My own answer doesn't work. I would have guessed it's because when a gas has pressure the kinetic energy adds to the rest mass of a given ...
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3answers
1k views

Can spacetime be non-orientable?

This question asks what constraints there are on the global topology of spacetime from the Einstein equations. It seems to me the quotient of any global solution can in turn be a global solution. In ...
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5answers
523 views

Binary Black Hole Solution of General Relativity?

This is rather a technical question for experts in General Relativity. An accessible link would be an accepable answer, although any additional discussion is welcome. GR has well known solutions ...
12
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2answers
806 views

If two ultra-relativistic billiard balls just miss, will they still form a black hole?

This forum seems to agree that a billiard ball accellerated to ultra-relativistic speeds does not turn into a black hole. (See recent question "If a 1kg mass was accelerated close to the speed of ...
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2answers
407 views

Expansion of the space-time metric [duplicate]

If the space-time metric is expanding with the expansion of the universe, if I could travel back in time, would I be less dense than the matter in that previous era?
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3answers
456 views

References for ADM formalism and cosmological perturbation theory [closed]

What would you consider the best online resources for learning the 3+1 ADM formalism and gauge invariant perturbation theory in cosmology? (Assuming intermediate level GR and QFT familiarity)
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3answers
229 views

A flyby of orbiting supermassive black holes

Consider two supermassive black holes of equal mass orbiting about their common centre of mass. Is it the case that a free-fall trajectory along the axis of rotation would be outside of either event ...
4
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8answers
612 views

Is relativity necessary for the existence of life?

If the universe didn't have the relativity principle, would it be able to support life? Life consists of very complicated organisms. The operation of these organisms depends on the laws of physics. ...
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4answers
3k views

Is there a maximum possible acceleration?

I'm thinking equivalence principle, possibilities of unbounded space-time curvature, quantum gravity ...
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5answers
837 views

Should a neutron fall faster than a proton?

If you drop a proton and a neutron in a gravitational field, they both fall, but the proton has a charge and accelerating charges radiate energy, so that leaves less kinetic energy for the proton and ...
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7answers
2k views

What determines which frames are inertial frames?

I understand that you can (in principle) measure whether "free particles" (no forces) experience accelerations in order to tell whether a frame is inertial. But fundamentally, what determines which ...
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6answers
543 views

How Does Hubble's Expansion Affect Two Rope-Tied Galaxies?

Suppose we have two galaxies that are sufficiently far apart so that the distance between them increases due to Hubble's expansion. If I were to connect these two galaxies with a rope, would there be ...
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5answers
471 views

Black Hole Singularities

If two black holes collide and then evaporate, do they leave behind two naked sigularities ore? If there are two, can we know how they interact?
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8answers
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How exactly does curved space-time describe the force of gravity?

I understand that people explain (in layman's terms at least) that the presence of mass "warps" space-time geometry, and this causes gravity. I have also of course heard the analogy of a blanket or ...
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2answers
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Does the equivalence between inertial and gravitational mass imply anything about the Higgs mechanism?

For example: the role it might play in a theory of quantum gravity (ie causing space-time curvature)? I realize that inertial mass can result from binding energy alone. Has the equivalence principle ...
8
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3answers
660 views

Special Relativistic approximation to GR

Some time ago I was talking to a professor in college about some of the fundamental aspects and origin of General Relativity. I was surprised to learn, in fact, that a pretty good approximation to GR ...
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4answers
1k views

Shape of the universe?

What is the exact shape of the universe? I know of the balloon analogy, and the bread with raisins in it. These clarify some points, like how the universe can have no centre, and how it can expand ...
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3answers
2k views

Wormholes & Time Machines - for *experts* in GR/maths

EDIT: Further clarification in the context of answers/comments received to 20 Jan has been appended EDIT: 21 Jan - Response to the Lubos Expansion appended [in progress, not yet complete] EDIT: 23 ...
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5answers
3k views

Total energy of the Universe

In popular science books and articles, I keep running into the claim that the total energy of the Universe is zero, "because the positive energy of matter is cancelled out by the negative energy of ...
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7answers
3k views

Is it theoretically possible to shield gravitational fields or waves?

Electromagnetic waves can be shielded by a perfect conductor. What about gravitational fields or waves?
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2answers
1k views

What does “foliation” mean in the context of a “foliation of spacetime?”

I've seen foliation used in the context of "foliation of spacetime" here and elsewhere in papers and such. Generally defined in reference to a "sequence of spatial hypersurfaces." But I don't know ...
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1answer
782 views

How do I calculate the (apparent) gravitational pull with General Relativity?

Assume a static metric with (known) components $g_{\mu\nu}$. I'd like to know what is the gravitational pull $g$ of a test particle placed on an arbitrary point $X$. The gravitational pull being ...
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5answers
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What is the conserved quantity of a scale-invariant universe?

Consider that we have a system described by a wavefunction psi(x). We then make an exact copy of the system, and anything associated with it, (including the inner cogs and gears of the elementary ...
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2answers
553 views

“Space” in General Relativity and “vacuum” in Standard Model, is it the same thing?

And expansion of space is equal to expansion of vacuum?
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3answers
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Energy conservation in General Relativity

I understand that energy conservation is not a rule in general relativity, but I'd like to know under what circumstances it can still be possible. In other words, when is it possible to associate a ...
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5answers
3k views

How is the classical twin paradox resolved?

I read a lot about the classical twin paradox recently. What confuses me is that some authors claim that it can be resolved within SRT, others say that you need GRT. Now, what is true (and why)?
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2answers
460 views

How do you explain the observed fact that “black hole” objects move?

As per Newton objects with mass attract each other, and per Einstein this is further explained by saying that mass warps space-time. So a massive object makes a "dent" into space-time, a gravity well. ...
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4answers
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What is the physical meaning of the connection and the curvature tensor?

Regarding general relativity: What is the physical meaning of the Christoffel symbol ($\Gamma^i_{\ jk}$)? What are the (preferably physical) differences between the Riemann curvature tensor ($R^i_{\ ...
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4answers
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Why is the equivalence principle so important to general relativity?

In its simplest form, equivalence principle states that the inertial mass and the gravitational mass should be the same. This is easy to understand. But why is it so important to the formulation of ...
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3answers
262 views

Calculating absolute speed of a relative object [closed]

Say you pick a point on the Earth. The earth spins at some constant $x (I don't know how fast, sorry). Now, that point has a different relative speed to a fixed point on Earth's orbit as it revolves ...
5
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1answer
388 views

Quantum Gravity and Calculations of Mercury's Perihelion

In an astronomy forum that I frequent, I have been having a discussion where the state of quantum gravity research came up. I claimed that Loop Quantum Gravity theories couldn't prove GR in the ...
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0answers
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What's the relationship between mass and time? [closed]

This question has arisen from a wish to understand an end-of-universe scenario: heat death. Are time and mass intrinsically linked? If so, does time "run slower" (whatever that may mean) in a ...
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7answers
2k views

How precisely does a star collapse into a black hole?

I think we all heard general statements like "once big enough star burns out there is nothing to prevent the gravitational collapse ending in a black hole". But I can't remember even seeing the ...
6
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2answers
1k views

What does it mean that the universe is “infinite”?

This question is about cosmology and general relativity. I understand the difference between the universe and the observable universe. What I am not really clear about is what is meant when I read ...
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3answers
770 views

Why space expansion affects matter?

If space itself is expanding, then why would it have any effect on matter (separates distant galaxies)? Space is "nothing", and if "nothing" becomes bigger "nothing" it's still a "nothing" that ...